I am generally interested in understanding of the cooperative dynamics of powder and relationship between the macroscopic behavior of granular materials and their microstructures. My research interests include:
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Granular materials are large assemblies of solid macroscopic particles characterized by a loss of energy whenever the particles interact. If they are noncohesive, the forces between them are strictly repulsive. The particles are usually surrounded by a fluid, most often air, which may play a role in the dynamics of the systems. The constituents that compose granular material must be large enough such that they are not subject to thermal motion fluctuations. Thus, the lower size limit for grains in granular material is about 1 micrometer. Examples of such materials include sand, stones, soil, ores, pharmaceuticals, and variety of chemicals. Powders are a special class of granular material due to their small particle size, which makes them more cohesive and more easily suspended in a gas. Granular materials are commercially important in applications as diverse as pharmaceutical industry, agriculture, and energy production. Granular materials are ubiquitous in nature and are the second-most manipulated material in industry (the first one is water).
At the root of the unique status of granular materials are two characteristic: ordinary temperature plays no role, and the interactions between grains are dissipative because of static friction and the inelasticity of collisions. There are no long-range interactions between individual grains or between individual grains and the walls of a confining container. Depending on the average energy of the individual grains they may exhibit the properties of solids, liquids, or gases. When the average energy of the individual grains is low and the grains are fairly stationary relative to each other, the granular material acts like a solid. When the granular matter is driven and energy is fed into the system (such as by shaking) such that the grains are not in constant contact with each other, the granular material is said to fluidize and enter a liquid-like state. If the granular material is driven harder such that contacts between the grains become highly infrequent, the material enters a gaseous state.
Yet despite this seeming simplicity, a granular material behaves differently from any of the other familiar forms of matter - solids, liquids, or gases. For instance one can cite internal stress fluctuations, strain localization, non-Newtonian rheology, spontaneous clusterization, size segregation or spatial pattern creations. All these phenomena have no equivalent in classical solid- or liquid-state physics. Granular materials dissipate energy quickly, so techniques of statistical mechanics that assume conservation of energy are of limited use. Therefore, granular material should be considered an additional state of matter in its own right. Attempts toward understanding and controlling both static and dynamic properties of granular materials are thus of highest interest to many fields of physics, applied sciences and engineering.
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I am generally interested in understanding of the cooperative dynamics of powder and relationship between the macroscopic behavior of granular materials and their microstructures. My research interests include: |
Abstract: The transport of trace granular gas (swarm) in a carrier granular fluid is studied by means of Boltzmann--Lorentz kinetic equation. Time-dependent perturbation theory is used to follow the evolution of the granular swarm from an arbitrary initial distribution. A non-hydrodynamic extension of the diffusion equation is derived, with transport coefficients that are time dependent and implicitly depend on the wave vector. Transport coefficients of any order are obtained as velocity moments of the solutions of the corresponding kinetic equations derived from the Boltzmann--Lorentz equation. For the special case of initial distribution of swarm particles, transport coefficients are identified as time derivatives of the moments of the number density. Finally the granular particle transport theory is extended by the introduction of the concept of non-particle conserving collisions.
Abstract: We study experimentally the creeping penetration of guest (percolating) grains through densely packed granular media in two dimensions. The evolution of the system of the guest grains during the penetration is studied by image analysis. To quantify the changes in the internal structure of the packing we use Vorono\"{i} tessellation and certain shape factor which is a clear indicator of the presence of different underlying substructures (domains). We first consider the impact of the effective gravitational acceleration on upward penetration of grains. It is found that the higher effective gravity increases the resistance to upward penetration and enhances structural organization in the system of the percolating grains. We also focus our attention on the dependence of the structural rearrangements of percolating grains on some parameters like the polydispersity and the initial packing fraction of the host granular system. It is found that anisotropy of penetration is larger in the monodisperse case than in the bidisperse one, for the same value of packing fraction of host medium. Compaction of initial host granular packing also increases anisotropy of penetration of guest grains. When a binary mixture of large and small guest grains is penetrated into host granular medium, we observe a size segregation patterns.
Abstract: We investigate, by numerical simulation, the dynamical response of a granular system to an abrupt change in shaking intensity within the framework of the reversibile random sequential adsorption models. We analyse the two-dimensional lattice model in which, in addition to the adsorption-desorption process, there is diffusion of the adsorbed particles on the surface. Our model reproduces qualitatively the densification kinetics and the memory effects of vibrated granular materials. An interpretation of the simulation results is provided by the analysis of the insertion probability function. The importance of the diffusional relaxation is discussed. We conclude that a complex time-evolution of the density could be explained as a consequence of the variation of the diffusion rate during the compaction.
Abstract: Reversible random sequential adsorption of objects of various shapes on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The growth of the coverage $\rho(t)$ above the jamming limit to its steady-state value $\rho_{\infty}$ is described by a pattern $\rho(t)= \rho_{\infty} - \Delta\rho E_\beta [-(t/\tau)^\beta]$, where $E_\beta$ denotes the Mittag-Leffler function of order $\beta\in(0,1)$. The parameter $\tau$ is found to decay with the desorption probability $P_-$ according to a power law $\tau=A\;P_-^{-\gamma}$. The exponent $\gamma$ is the same for all shapes, $\gamma = 1.29 \pm 0.01$, but the parameter $A$ depends only on the order of symmetry axis of the shape. Finally, we present the possible relevance of the model to the compaction of granular objects of various shapes.
Abstract: We perform numerical simulation of a lattice model for the compaction of a granular material based on the idea of reversible random sequential adsorption. Reversible random sequential adsorption of objects of various shapes on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The growth of the coverage $\rho(t)$ above the jamming limit to its steady-state value $\rho_{\infty}$ is described by a pattern $\rho(t)= \rho_{\infty} - \Delta\rho E_\beta [-(t/\tau)^\beta]$, where $E_\beta$ denotes the Mittag-Leffler function of order $\beta\in(0,1)$. For the first time, the parameter $\tau$ is found to decay with the desorption probability $P_-$ according to a power law $\tau=A\;P_-^{-\gamma}$. Exponent $\gamma$ is the same for all shapes, $\gamma = 1.29 \pm 0.01$, but parameter $A$ depends only on the order of symmetry axis of the shape. Finally, we present the possible relevance of the model to the compaction of granular objects of various shapes.
Abstract: We study by numerical simulation the compaction dynamics of frictional hard disks in two dimensions, subjected to vertical shaking. Shaking is modeled by a series of vertical expansion of the disk packing, followed by dynamical recompression of the assembly under the action of gravity. The second phase of the shake cycle is based on an efficient event-driven molecular-dynamics algorithm. We analyze the compaction dynamics for various values of friction coefficient and coefficient of normal restitution. We find that the time evolution of the density is described by $\rho(t)=\rho_\infty - \Delta\rho\; E_\alpha \left[ -(t/\tau)^\alpha \right]$, where $E_\alpha$ denotes the Mittag-Leffler function of order $0 < \alpha < 1$. The parameter $\tau$ is found to decay with tapping intensity $\Gamma$ according to a power law $\tau\propto\Gamma^{-\gamma}$, where parameter $\gamma$ is almost independent on the material properties of grains. Also, an expression for the grain mobility during compaction process has been obtained. We characterize the local organization of disks in terms of contact connectivity and distribution of the Delaunay `free' volumes. Our analysis at microscopic scale provides evidence that compaction is mainly due to decrease of the number of the largest pores. An interpretation of the memory effects observed for a discontinuous shift in tapping intensity $\Gamma$ is provided by the analysis of the time evolution of connectivity numbers and volume distribution of pores.
Abstract: We study by numerical simulation the compaction dynamics of frictional hard disks in two dimensions, subjected to vertical shaking. Shaking is modeled by a series of vertical expansion of the disk packing, followed by dynamical recompression of the assembly under the action of gravity. The second phase of the shake cycle is based on an efficient event-driven molecular-dynamics algorithm. We analyze the compaction dynamics for various values of friction coefficient and coefficient of normal restitution. We find that the time evolution of the density is described by $\rho(t)=\rho_\infty - \Delta\rho\; E_\alpha \left[ -(t/\tau)^\alpha \right]$, where $E_\alpha$ denotes the Mittag-Leffler function of order $0 < \alpha < 1$. The parameter $\tau$ is found to decay with tapping intensity $\Gamma$ according to a power law $\tau\propto\Gamma^{-\gamma}$, where parameter $\gamma$ is almost independent on the material properties of grains. Also, an expression for the grain mobility during compaction process has been obtained.
Abstract: We study the compaction dynamics of frictional hard disks in two dimensions, subjected to vertical shaking, by numerical simulation. Shaking is modeled by a series of vertical expansions of the disk packing, followed by dynamical recompression of the assembly under the action of gravity. The second phase of the shake cycle is based on an efficient event-driven molecular-dynamics algorithm. We analyze the compaction dynamics for various values of the friction coefficient and the coefficient of normal restitution. The granular organization at local level was studied by analyzing the shape factor \xi of the local volumes, associated with a natural way of subdividing the volume into local parts - the Voronoi partition. It gives a clear physical picture of the competition between less and more ordered domains of particles during the compaction. We calculate the distribution of the shape-factor for packings at different stages of the compaction process. We have also investigated a two-dimensional granular medium experimentally. We prepared the granular packings of metallic cylinders of diameters 4, 5, and 6 mm. The distributions of the shape-factor obtained numerically for various tapping intensities are consistent with our experimental results.
Abstract: We examine numerically the density relaxation of frictional hard disks in two dimensions (2D), subjected to vertical shaking. Dynamical recompression of the packing under the action of gravity is based on an efficient event-driven molecular-dynamics algorithm. To quantify the changes in the internal structure of packing during the compaction, we use the Voronoi tessellation and a certain shape factor which is a clear indicator of the presence of different domains in the packing. It is found that the narrowing of the probability distribution of the shape factor during the compaction is in accordance with the fact that the packings of monodisperse hard disks spontaneously assemble into regions of local crystalline order. An interpretation of the memory effects observed for a sudden perturbation of the tapping intensity is provided by the analysis the accompanying transformations of disk packings at a `microscopic' level. In addition, we investigate the distributions of the shape factor in a 2D granular system of metallic disks experimentally, and compare them with the simulation results.
Abstract: We present an approach to granular compaction based on subordination of stochastic processes. In order to imitate, in a very simplified way, the compaction dynamics of granular material under tapping, we impose that particles switch stochastically between the two possible orientational states characterizing the average volumes of the grain in the presence of other grains. The main physical idea of our approach is that the interaction of grains with their environment is taken into account with the aid of the temporal subordination. Accordingly, we assume that the time intervals between the consecutive grain's reorientations are governed by a certain waiting-time distribution $\psi(t)$. It is demonstrated how the presence of the trapping events leads to the macroscopic observation of slow compaction dynamics, described by an exact fractional kinetic equation. We also perform numerical simulations to examine our analytical result. In addition, we reproduce the memory effects numerically by considering the response of the system to the abrupt change in the external excitation.
Abstract: We consider the impact of the effective gravitational acceleration on microstructural properties of granular packings through experimental studies of spherical granular materials saturated within fluids of varying density. We characterize the local organization of spheres in terms of contact connectivity, distribution of the Delaunay free volumes, and the shape factor (parameter of nonsphericity) of the Voronoi polygons. The shape factor gives a clear physical picture of the competition between less and more ordered domains of particles in experimentally obtained packings. As the effective gravity increases, the probability distribution of the shape factor becomes narrower and more localized around the lowest values of the shape factor corresponding to regular hexagon. It is found that curves of the pore distributions are asymmetric with a long tail on the right-hand side, which progressively reduces while the effective gravity gets stronger for lower densities of interstitial fluid. We show that the distribution of local areas (Voronoi cells) broadens with decreasing value of the effective gravity due to the formation of lose structures such as large pores and chainlike structures (arches or bridges). Our results should be particularly helpful in testing the newly developed simulation techniques involving liquid-related forces associated with immersed granular particles.
Abstract: We report on measurements of the electrical conductivity on a two-dimensional packing of metallic disks when a stable current of $\sim 1$~mA flows through the system. At low applied currents, the conductance $\sigma$ is found to increase by a pattern $\sigma(t)= \sigma_{\infty} - \Delta\sigma E_\alpha [-(t/\tau)^\alpha]$, where $E_\alpha$ denotes the Mittag-Leffler function of order $\alpha\in(0,1)$. By changing the inclination angle $\theta$ of the granular bed from horizontal, we have studied the impact of the effective gravitational acceleration $g_\text{eff}=g\sin\theta$ on the relaxation features of the conductance $\sigma(t)$. The characteristic timescale $\tau$ is found to grow when effective gravity $g_\text{eff}$ decreases. By changing both the distance between the electrodes and the number of grains in the packing, we have shown that the long term resistance decay observed in the experiment is related to local micro-contacts rearrangements at each disk.By focusing on the electro-mechanical processes that allow both creation and breakdown of micro-contacts between two disks, we present an approach to granular conduction based on subordination of stochastic processes. In order to imitate, in a very simplified way, the conduction dynamics of granular material at low currents, we impose that the micro-contacts at the interface switch stochastically between two possible states, \emph{``on''} and \emph{``off''}, characterizing the conductivity of the micro-contact. We assume that the time intervals between the consecutive changes of state are governed by a certain waiting-time distribution. It is demonstrated how the microscopic random dynamics regarding the micro-contacts leads to the macroscopic observation of slow conductance growth, described by an exact fractional kinetic equations.
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